Optimal electronic musical instruments

For many musical instruments, a musician depresses various combinations of keys in order to play the notes in the instrument’s range. For traditional (or acoustic) instruments of this type (e.g., woodwinds and most brass), the ways in which the combinations of keys can be assigned to the notes are limited by physics. However, for electronic instruments of this type, there are essentially no such limitations. In this paper, we exploit this freedom and present several designs for electronic instruments which are optimally easy to play; that is, the total movement of the fingers when playing some common sequences of notes (i.e., various, general collections of scales) is minimized. Our designs are built upon Gray codes, which are used in digital communications.